Trump, who secured an emphatic 5-0 win over Eden Sharav in the previous round, registered the third maximum of his career in the fifth frame to open up a 4-1 advantage.
Tian reduced the deficit to 4-3 with breaks of 60 and 63, but Trump held his nerve to close out the match in the eighth frame.
Trump told the World Snooker website: "I've had a lot of good chances recently and it was nice to make a 147 on the TV table. The next frame I potted a good ball to get in.
"I then split the pack well but unfortunately the red went in. I probably would have made another century if that didn't happen, you need a bit of luck in those situations.
"After that he played well and things like that can change games, so I'm happy to get through."
Mark Williams battled back from 4-1 down to defeat John Higgins 5-4 in a thrilling contest.
The two-time world champion won the sixth frame before reeling off breaks of 66, 60 and 79 to edge out Higgins.
Williams will face Shaun Murphy, a 5-1 winner against Michael White, in the quarter-finals.
World champion Mark Selby edged a tense final-frame decider against Andrew Higginson and will next face Stephen Maguire, a comfortable 5-1 winner over Daniel Wells.
Mark Joyce was unable to follow up his impressive win over Ronnie O'Sullivan as he slipped to a 5-3 defeat against Ding Junhui.
The Chinese player will take on Kyren Wilson, who saw off former world champion Stuart Bingham 5-2, for a place in the semi-finals.
Trump's next opponent is Hossein Vafaei, who overcame Rory McLeod 5-3 earlier in the day.
Thursday results & remaining tournament schedule
Thursday March 30
Afternoon Session (0700 GMT)
Third Round (Best of 9 frames)
Judd Trump 5-3 Tian Pengfei (Match 49) * TRUMP HITS 147
Rory McLeod 3-5 Hossein Vafaei (Match 50)
Shaun Murphy 5-1 Michael White (Match 51)
Mark Williams 5-4 John Higgins (Match 52)
Evening Session (1230 GMT)
Third Round (Best of 9 frames)
Stuart Bingham 2-5 Kyren Wilson (Match 53)
Mark Joyce 3-5 Ding Junhui (Match 54)
Daniel Wells 1-5 Stephen Maguire (Match 55)
Andrew Higginson 4-5 Mark Selby (Match 56)
Friday March 31
Afternoon Session (0700 GMT)
Quarter-Finals (Best of 9 frames)
TV Coverage: Eurosport 1/Quest
Judd Trump v Hossein Vafaei (QF 1)
Shaun Murphy v Mark Williams (QF 2)
Evening Session (1230 GMT)
Quarter-Finals (Best of 9 frames)
TV Coverage: Eurosport 1/Quest
Kyren Wilson v Ding Junhui (QF 3)
Stephen Maguire v Mark Selby (QF 4)
Saturday April 1
Afternoon Session (0700 GMT)
Semi-Finals (Best of 11 frames)
TV Coverage: Eurosport 1/Quest
Trump/Vafaei v Murphy/Williams (SF 1)
Evening Session (1230 GMT)
Semi-Finals (Best of 11 frames)
TV Coverage: Eurosport 1/Quest
Wilson/Ding v Maguire/Selby (SF 1)
Sunday April 2
Afternoon Session (0700 GMT)
Final, first session (Best of 19 frames)
TV Coverage: Eurosport 1/Quest
Winner SF 1 v Winner SF 2
Evening Session (1230 GMT)
Final, second session (Best of 19 frames)
TV Coverage: Eurosport 1/Quest
Winner SF 1 v Winner SF 2
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